Firstly, the e-residency team is not the Estonian government. I don't know the details, but to me it seems like someone just gave a bunch of kids some money and said: "Hey, go promote our country!"
If they were the Estonian government, they certainly wouldn't have to ask a private company for advice.
Anyway, that article is about director's fees. Director's fees are not salaries, they are neither dividend nor salary. They are also taxed differently for Estonian tax residents - I believe it used to be advantageous for Estonian tax residents to take payments through director's fees instead of salary, but that changed a couple years ago. I don't know the details.
Even the article you linked to explains that salaries of non-residents are not taxed in Estonia, and you can receive a salary even as a director, especially if you have provided other services than just managing the company.
You may also be able to invoice the company for services provided.
If someone is serious about this, I would strongly advise to talk to an Estonian accountant about this and not blindly trust some very general information.